TSTP Solution File: GRP129-4.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:40:13 EDT 2023
% Result : Unsatisfiable 25.35s 11.92s
% Output : CNFRefutation 25.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 28
% Syntax : Number of formulae : 269 ( 111 unt; 7 typ; 0 def)
% Number of atoms : 682 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 628 ( 208 ~; 420 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 171 (; 171 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_95,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_83,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_99,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_89,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_101,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_97,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_77,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_43,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y)
| product(e_4,X,Y) ),
file(unknown,unknown) ).
tff(f_79,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_74,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y)
| product(X,e_4,Y) ),
file(unknown,unknown) ).
tff(f_65,axiom,
! [Y,X,Z1,Z2] :
( product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| ~ product(X,Z1,Z2) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_76,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_115,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_139,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_81,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X,Z1,Z2,Y] :
( product(X,Z1,Z2)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_147,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(X,Z1,Z2)
| product(Z1,Y,Z2) ),
file(unknown,unknown) ).
tff(f_75,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(c_34,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_22,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_38,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_28,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_40,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_36,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_16,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( product(e_4,X_1,Y_2)
| product(e_3,X_1,Y_2)
| product(e_2,X_1,Y_2)
| product(e_1,X_1,Y_2)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_18,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_10,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( product(X_3,e_4,Y_4)
| product(X_3,e_3,Y_4)
| product(X_3,e_2,Y_4)
| product(X_3,e_1,Y_4)
| ~ group_element(Y_4)
| ~ group_element(X_3) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_76,plain,
! [X_57,Y_58] :
( product(X_57,e_4,Y_58)
| product(X_57,e_3,Y_58)
| product(X_57,e_2,Y_58)
| product(X_57,e_1,Y_58)
| ~ group_element(Y_58)
| ~ group_element(X_57) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_6,plain,
! [X_6,Z1_7,Z2_8,Y_5] :
( ~ product(X_6,Z1_7,Z2_8)
| ~ product(Z1_7,Y_5,Z2_8)
| product(Y_5,X_6,Z1_7) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_319,plain,
! [Y_100,Y_101,X_102] :
( ~ product(e_4,Y_100,Y_101)
| product(Y_100,X_102,e_4)
| product(X_102,e_3,Y_101)
| product(X_102,e_2,Y_101)
| product(X_102,e_1,Y_101)
| ~ group_element(Y_101)
| ~ group_element(X_102) ),
inference(resolution,[status(thm)],[c_76,c_6]) ).
tff(c_324,plain,
! [X_102,Y_4] :
( product(e_4,X_102,e_4)
| product(X_102,e_3,Y_4)
| product(X_102,e_2,Y_4)
| product(X_102,e_1,Y_4)
| ~ group_element(X_102)
| product(e_4,e_3,Y_4)
| product(e_4,e_2,Y_4)
| product(e_4,e_1,Y_4)
| ~ group_element(Y_4)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_4,c_319]) ).
tff(c_331,plain,
! [X_102,Y_4] :
( product(e_4,X_102,e_4)
| product(X_102,e_3,Y_4)
| product(X_102,e_2,Y_4)
| product(X_102,e_1,Y_4)
| ~ group_element(X_102)
| product(e_4,e_3,Y_4)
| product(e_4,e_2,Y_4)
| product(e_4,e_1,Y_4)
| ~ group_element(Y_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_324]) ).
tff(c_4126,plain,
! [Y_4] :
( product(e_4,e_4,e_4)
| ~ group_element(e_4)
| product(e_4,e_2,Y_4)
| product(e_4,e_1,Y_4)
| ~ group_element(Y_4)
| product(e_4,e_3,Y_4) ),
inference(factorization,[status(thm),theory(equality)],[c_331]) ).
tff(c_4129,plain,
! [Y_4] :
( product(e_4,e_4,e_4)
| product(e_4,e_2,Y_4)
| product(e_4,e_1,Y_4)
| ~ group_element(Y_4)
| product(e_4,e_3,Y_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4126]) ).
tff(c_4406,plain,
product(e_4,e_4,e_4),
inference(splitLeft,[status(thm)],[c_4129]) ).
tff(c_44,plain,
! [W_17,Z_18,X_15,Y_16] :
( equalish(W_17,Z_18)
| ~ product(X_15,Y_16,Z_18)
| ~ product(X_15,Y_16,W_17) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_4653,plain,
! [W_158] :
( equalish(W_158,e_4)
| ~ product(e_4,e_4,W_158) ),
inference(resolution,[status(thm)],[c_4406,c_44]) ).
tff(c_4724,plain,
! [Y_2] :
( equalish(Y_2,e_4)
| product(e_3,e_4,Y_2)
| product(e_2,e_4,Y_2)
| product(e_1,e_4,Y_2)
| ~ group_element(Y_2)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_2,c_4653]) ).
tff(c_4794,plain,
! [Y_2] :
( equalish(Y_2,e_4)
| product(e_3,e_4,Y_2)
| product(e_2,e_4,Y_2)
| product(e_1,e_4,Y_2)
| ~ group_element(Y_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4724]) ).
tff(c_14,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_42,plain,
! [X_13,Y_14] :
( product(X_13,Y_14,e_4)
| product(X_13,Y_14,e_3)
| product(X_13,Y_14,e_2)
| product(X_13,Y_14,e_1)
| ~ group_element(Y_14)
| ~ group_element(X_13) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_48,plain,
! [W_23,Z_26,Y_24,X_25] :
( equalish(W_23,Z_26)
| ~ product(Z_26,Y_24,X_25)
| ~ product(W_23,Y_24,X_25) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_4801,plain,
! [W_159] :
( equalish(W_159,e_4)
| ~ product(W_159,e_4,e_4) ),
inference(resolution,[status(thm)],[c_4406,c_48]) ).
tff(c_4861,plain,
! [X_13] :
( equalish(X_13,e_4)
| product(X_13,e_4,e_3)
| product(X_13,e_4,e_2)
| product(X_13,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_13) ),
inference(resolution,[status(thm)],[c_42,c_4801]) ).
tff(c_4895,plain,
! [X_13] :
( equalish(X_13,e_4)
| product(X_13,e_4,e_3)
| product(X_13,e_4,e_2)
| product(X_13,e_4,e_1)
| ~ group_element(X_13) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4861]) ).
tff(c_93,plain,
! [W_17,Y_58,X_57] :
( equalish(W_17,Y_58)
| ~ product(X_57,e_4,W_17)
| product(X_57,e_3,Y_58)
| product(X_57,e_2,Y_58)
| product(X_57,e_1,Y_58)
| ~ group_element(Y_58)
| ~ group_element(X_57) ),
inference(resolution,[status(thm)],[c_76,c_44]) ).
tff(c_4426,plain,
! [Y_58] :
( equalish(e_4,Y_58)
| product(e_4,e_3,Y_58)
| product(e_4,e_2,Y_58)
| product(e_4,e_1,Y_58)
| ~ group_element(Y_58)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_4406,c_93]) ).
tff(c_5767,plain,
! [Y_168] :
( equalish(e_4,Y_168)
| product(e_4,e_3,Y_168)
| product(e_4,e_2,Y_168)
| product(e_4,e_1,Y_168)
| ~ group_element(Y_168) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4426]) ).
tff(c_31327,plain,
! [Y_321,Y_322] :
( ~ product(e_3,Y_321,Y_322)
| product(Y_321,e_4,e_3)
| equalish(e_4,Y_322)
| product(e_4,e_2,Y_322)
| product(e_4,e_1,Y_322)
| ~ group_element(Y_322) ),
inference(resolution,[status(thm)],[c_5767,c_6]) ).
tff(c_31386,plain,
( product(e_4,e_4,e_3)
| equalish(e_4,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_4895,c_31327]) ).
tff(c_31534,plain,
( product(e_4,e_4,e_3)
| equalish(e_4,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_31386]) ).
tff(c_31535,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_40,c_31534]) ).
tff(c_31631,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_31535]) ).
tff(c_20,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_4857,plain,
! [X_3] :
( equalish(X_3,e_4)
| product(X_3,e_3,e_4)
| product(X_3,e_2,e_4)
| product(X_3,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X_3) ),
inference(resolution,[status(thm)],[c_4,c_4801]) ).
tff(c_4892,plain,
! [X_3] :
( equalish(X_3,e_4)
| product(X_3,e_3,e_4)
| product(X_3,e_2,e_4)
| product(X_3,e_1,e_4)
| ~ group_element(X_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4857]) ).
tff(c_8,plain,
! [Y_12,X_9,Z1_10,Z2_11] :
( ~ product(Y_12,X_9,Z1_10)
| ~ product(Z1_10,Y_12,Z2_11)
| product(X_9,Z1_10,Z2_11) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_33400,plain,
! [Z2_329] :
( ~ product(e_1,e_3,Z2_329)
| product(e_4,e_1,Z2_329) ),
inference(resolution,[status(thm)],[c_31631,c_8]) ).
tff(c_46,plain,
! [W_20,Z_22,X_19,Y_21] :
( equalish(W_20,Z_22)
| ~ product(X_19,Z_22,Y_21)
| ~ product(X_19,W_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_4512,plain,
! [W_20] :
( equalish(W_20,e_4)
| ~ product(e_4,W_20,e_4) ),
inference(resolution,[status(thm)],[c_4406,c_46]) ).
tff(c_33481,plain,
( equalish(e_1,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[c_33400,c_4512]) ).
tff(c_33611,plain,
~ product(e_1,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_22,c_33481]) ).
tff(c_33669,plain,
( equalish(e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4892,c_33611]) ).
tff(c_33698,plain,
( equalish(e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_33669]) ).
tff(c_33699,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_33698]) ).
tff(c_37887,plain,
product(e_1,e_1,e_4),
inference(splitLeft,[status(thm)],[c_33699]) ).
tff(c_39457,plain,
! [Y_349] :
( ~ product(e_1,Y_349,e_4)
| product(Y_349,e_1,e_1) ),
inference(resolution,[status(thm)],[c_37887,c_6]) ).
tff(c_39521,plain,
product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[c_37887,c_39457]) ).
tff(c_38005,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_1,e_1,W_17) ),
inference(resolution,[status(thm)],[c_37887,c_44]) ).
tff(c_39567,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_39521,c_38005]) ).
tff(c_39595,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_39567]) ).
tff(c_39597,plain,
~ product(e_1,e_1,e_4),
inference(splitRight,[status(thm)],[c_33699]) ).
tff(c_95,plain,
! [X_59,Y_60] :
( product(e_4,X_59,Y_60)
| product(e_3,X_59,Y_60)
| product(e_2,X_59,Y_60)
| product(e_1,X_59,Y_60)
| ~ group_element(Y_60)
| ~ group_element(X_59) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_111,plain,
! [W_20,X_59,Y_60] :
( equalish(W_20,X_59)
| ~ product(e_4,W_20,Y_60)
| product(e_3,X_59,Y_60)
| product(e_2,X_59,Y_60)
| product(e_1,X_59,Y_60)
| ~ group_element(Y_60)
| ~ group_element(X_59) ),
inference(resolution,[status(thm)],[c_95,c_46]) ).
tff(c_4440,plain,
! [X_59] :
( equalish(e_4,X_59)
| product(e_3,X_59,e_4)
| product(e_2,X_59,e_4)
| product(e_1,X_59,e_4)
| ~ group_element(e_4)
| ~ group_element(X_59) ),
inference(resolution,[status(thm)],[c_4406,c_111]) ).
tff(c_4505,plain,
! [X_59] :
( equalish(e_4,X_59)
| product(e_3,X_59,e_4)
| product(e_2,X_59,e_4)
| product(e_1,X_59,e_4)
| ~ group_element(X_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4440]) ).
tff(c_50,plain,
! [Z1_29,Y_27,Z2_30,X_28] :
( product(Z1_29,Y_27,Z2_30)
| ~ product(X_28,Z1_29,Z2_30)
| ~ product(Y_27,X_28,Z1_29) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_33719,plain,
! [Y_330] :
( product(e_4,Y_330,e_1)
| ~ product(Y_330,e_3,e_4) ),
inference(resolution,[status(thm)],[c_31631,c_50]) ).
tff(c_33790,plain,
( product(e_4,e_3,e_1)
| equalish(e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_4505,c_33719]) ).
tff(c_33920,plain,
( product(e_4,e_3,e_1)
| equalish(e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_33790]) ).
tff(c_33921,plain,
( product(e_4,e_3,e_1)
| product(e_2,e_3,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_33611,c_40,c_33920]) ).
tff(c_35005,plain,
product(e_2,e_3,e_4),
inference(splitLeft,[status(thm)],[c_33921]) ).
tff(c_39596,plain,
product(e_1,e_2,e_4),
inference(splitRight,[status(thm)],[c_33699]) ).
tff(c_41211,plain,
! [Y_356] :
( ~ product(e_2,Y_356,e_4)
| product(Y_356,e_1,e_2) ),
inference(resolution,[status(thm)],[c_39596,c_6]) ).
tff(c_41275,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_35005,c_41211]) ).
tff(c_4515,plain,
! [W_157] :
( equalish(W_157,e_4)
| ~ product(e_4,W_157,e_4) ),
inference(resolution,[status(thm)],[c_4406,c_46]) ).
tff(c_4584,plain,
! [X_1] :
( equalish(X_1,e_4)
| product(e_3,X_1,e_4)
| product(e_2,X_1,e_4)
| product(e_1,X_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_2,c_4515]) ).
tff(c_6300,plain,
! [X_174] :
( equalish(X_174,e_4)
| product(e_3,X_174,e_4)
| product(e_2,X_174,e_4)
| product(e_1,X_174,e_4)
| ~ group_element(X_174) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4584]) ).
tff(c_6409,plain,
! [W_17,X_174] :
( equalish(W_17,e_4)
| ~ product(e_3,X_174,W_17)
| equalish(X_174,e_4)
| product(e_2,X_174,e_4)
| product(e_1,X_174,e_4)
| ~ group_element(X_174) ),
inference(resolution,[status(thm)],[c_6300,c_44]) ).
tff(c_41328,plain,
( equalish(e_2,e_4)
| equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_41275,c_6409]) ).
tff(c_41375,plain,
( equalish(e_2,e_4)
| equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_41328]) ).
tff(c_41376,plain,
product(e_2,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_39597,c_22,c_28,c_41375]) ).
tff(c_35156,plain,
! [W_20] :
( equalish(W_20,e_3)
| ~ product(e_2,W_20,e_4) ),
inference(resolution,[status(thm)],[c_35005,c_46]) ).
tff(c_41416,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_41376,c_35156]) ).
tff(c_41469,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_41416]) ).
tff(c_41470,plain,
product(e_4,e_3,e_1),
inference(splitRight,[status(thm)],[c_33921]) ).
tff(c_49172,plain,
! [Y_382] :
( ~ product(e_3,Y_382,e_1)
| product(Y_382,e_4,e_3) ),
inference(resolution,[status(thm)],[c_41470,c_6]) ).
tff(c_49264,plain,
product(e_4,e_4,e_3),
inference(resolution,[status(thm)],[c_31631,c_49172]) ).
tff(c_4513,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_4,e_4,W_17) ),
inference(resolution,[status(thm)],[c_4406,c_44]) ).
tff(c_49361,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_49264,c_4513]) ).
tff(c_49487,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_49361]) ).
tff(c_49489,plain,
~ product(e_3,e_4,e_1),
inference(splitRight,[status(thm)],[c_31535]) ).
tff(c_49494,plain,
( equalish(e_1,e_4)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4794,c_49489]) ).
tff(c_49516,plain,
( equalish(e_1,e_4)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_49494]) ).
tff(c_49517,plain,
( product(e_2,e_4,e_1)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_49516]) ).
tff(c_49531,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_49517]) ).
tff(c_51064,plain,
! [Z2_389] :
( ~ product(e_1,e_1,Z2_389)
| product(e_4,e_1,Z2_389) ),
inference(resolution,[status(thm)],[c_49531,c_8]) ).
tff(c_51145,plain,
( equalish(e_1,e_4)
| ~ product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[c_51064,c_4512]) ).
tff(c_51275,plain,
~ product(e_1,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_22,c_51145]) ).
tff(c_51331,plain,
! [Y_390] :
( product(e_4,Y_390,e_1)
| ~ product(Y_390,e_1,e_4) ),
inference(resolution,[status(thm)],[c_49531,c_50]) ).
tff(c_51376,plain,
( product(e_4,e_3,e_1)
| equalish(e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4505,c_51331]) ).
tff(c_51443,plain,
( product(e_4,e_3,e_1)
| equalish(e_4,e_1)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_51376]) ).
tff(c_51444,plain,
( product(e_4,e_3,e_1)
| product(e_2,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_51275,c_36,c_51443]) ).
tff(c_52477,plain,
product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_51444]) ).
tff(c_49645,plain,
! [Y_27] :
( product(e_4,Y_27,e_1)
| ~ product(Y_27,e_1,e_4) ),
inference(resolution,[status(thm)],[c_49531,c_50]) ).
tff(c_52528,plain,
product(e_4,e_2,e_1),
inference(resolution,[status(thm)],[c_52477,c_49645]) ).
tff(c_54526,plain,
! [Y_401] :
( product(e_1,Y_401,e_4)
| ~ product(Y_401,e_2,e_1) ),
inference(resolution,[status(thm)],[c_52477,c_50]) ).
tff(c_54549,plain,
product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[c_52528,c_54526]) ).
tff(c_49648,plain,
! [W_17] :
( equalish(W_17,e_1)
| ~ product(e_1,e_4,W_17) ),
inference(resolution,[status(thm)],[c_49531,c_44]) ).
tff(c_54565,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_54549,c_49648]) ).
tff(c_54650,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_54565]) ).
tff(c_54652,plain,
~ product(e_2,e_1,e_4),
inference(splitRight,[status(thm)],[c_51444]) ).
tff(c_54651,plain,
product(e_4,e_3,e_1),
inference(splitRight,[status(thm)],[c_51444]) ).
tff(c_57106,plain,
! [Z2_410] :
( ~ product(e_1,e_4,Z2_410)
| product(e_3,e_1,Z2_410) ),
inference(resolution,[status(thm)],[c_54651,c_8]) ).
tff(c_57163,plain,
! [Z2_410] :
( equalish(Z2_410,e_4)
| equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1)
| ~ product(e_1,e_4,Z2_410) ),
inference(resolution,[status(thm)],[c_57106,c_6409]) ).
tff(c_57282,plain,
! [Z2_410] :
( equalish(Z2_410,e_4)
| equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ product(e_1,e_4,Z2_410) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_57163]) ).
tff(c_57347,plain,
! [Z2_411] :
( equalish(Z2_411,e_4)
| ~ product(e_1,e_4,Z2_411) ),
inference(negUnitSimplification,[status(thm)],[c_51275,c_54652,c_22,c_57282]) ).
tff(c_57356,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_49531,c_57347]) ).
tff(c_57442,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_57356]) ).
tff(c_57443,plain,
product(e_2,e_4,e_1),
inference(splitRight,[status(thm)],[c_49517]) ).
tff(c_58833,plain,
! [Z2_417] :
( ~ product(e_1,e_2,Z2_417)
| product(e_4,e_1,Z2_417) ),
inference(resolution,[status(thm)],[c_57443,c_8]) ).
tff(c_58911,plain,
( equalish(e_1,e_4)
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[c_58833,c_4512]) ).
tff(c_59042,plain,
~ product(e_1,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_22,c_58911]) ).
tff(c_12,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_4646,plain,
! [X_1] :
( equalish(X_1,e_4)
| product(e_3,X_1,e_4)
| product(e_2,X_1,e_4)
| product(e_1,X_1,e_4)
| ~ group_element(X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4584]) ).
tff(c_60105,plain,
! [Y_420] :
( product(e_4,Y_420,e_1)
| ~ product(Y_420,e_2,e_4) ),
inference(resolution,[status(thm)],[c_57443,c_50]) ).
tff(c_60144,plain,
( product(e_4,e_3,e_1)
| equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4646,c_60105]) ).
tff(c_60207,plain,
( product(e_4,e_3,e_1)
| equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_60144]) ).
tff(c_60208,plain,
( product(e_4,e_3,e_1)
| product(e_2,e_2,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_59042,c_28,c_60207]) ).
tff(c_60396,plain,
product(e_2,e_2,e_4),
inference(splitLeft,[status(thm)],[c_60208]) ).
tff(c_62684,plain,
! [Y_432] :
( ~ product(e_2,Y_432,e_4)
| product(Y_432,e_2,e_2) ),
inference(resolution,[status(thm)],[c_60396,c_6]) ).
tff(c_62747,plain,
product(e_2,e_2,e_2),
inference(resolution,[status(thm)],[c_60396,c_62684]) ).
tff(c_60517,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_2,e_2,W_17) ),
inference(resolution,[status(thm)],[c_60396,c_44]) ).
tff(c_62794,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_62747,c_60517]) ).
tff(c_62824,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_62794]) ).
tff(c_62826,plain,
~ product(e_2,e_2,e_4),
inference(splitRight,[status(thm)],[c_60208]) ).
tff(c_62825,plain,
product(e_4,e_3,e_1),
inference(splitRight,[status(thm)],[c_60208]) ).
tff(c_57,plain,
! [X_55,Y_56] :
( product(X_55,Y_56,e_4)
| product(X_55,Y_56,e_3)
| product(X_55,Y_56,e_2)
| product(X_55,Y_56,e_1)
| ~ group_element(Y_56)
| ~ group_element(X_55) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_72,plain,
! [Y_56,Y_5,X_55] :
( ~ product(Y_56,Y_5,e_4)
| product(Y_5,X_55,Y_56)
| product(X_55,Y_56,e_3)
| product(X_55,Y_56,e_2)
| product(X_55,Y_56,e_1)
| ~ group_element(Y_56)
| ~ group_element(X_55) ),
inference(resolution,[status(thm)],[c_57,c_6]) ).
tff(c_4410,plain,
! [X_55] :
( product(e_4,X_55,e_4)
| product(X_55,e_4,e_3)
| product(X_55,e_4,e_2)
| product(X_55,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_55) ),
inference(resolution,[status(thm)],[c_4406,c_72]) ).
tff(c_8428,plain,
! [X_188] :
( product(e_4,X_188,e_4)
| product(X_188,e_4,e_3)
| product(X_188,e_4,e_2)
| product(X_188,e_4,e_1)
| ~ group_element(X_188) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4410]) ).
tff(c_8611,plain,
! [W_17,X_188] :
( equalish(W_17,e_4)
| ~ product(e_4,X_188,W_17)
| product(X_188,e_4,e_3)
| product(X_188,e_4,e_2)
| product(X_188,e_4,e_1)
| ~ group_element(X_188) ),
inference(resolution,[status(thm)],[c_8428,c_44]) ).
tff(c_63786,plain,
( equalish(e_1,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_62825,c_8611]) ).
tff(c_63854,plain,
( equalish(e_1,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_63786]) ).
tff(c_63855,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_49489,c_22,c_63854]) ).
tff(c_66545,plain,
product(e_3,e_4,e_2),
inference(splitLeft,[status(thm)],[c_63855]) ).
tff(c_70977,plain,
! [Z2_458] :
( ~ product(e_2,e_3,Z2_458)
| product(e_4,e_2,Z2_458) ),
inference(resolution,[status(thm)],[c_66545,c_8]) ).
tff(c_57559,plain,
! [Y_5] :
( ~ product(e_4,Y_5,e_1)
| product(Y_5,e_2,e_4) ),
inference(resolution,[status(thm)],[c_57443,c_6]) ).
tff(c_63843,plain,
product(e_3,e_2,e_4),
inference(resolution,[status(thm)],[c_62825,c_57559]) ).
tff(c_64102,plain,
! [W_23] :
( equalish(W_23,e_3)
| ~ product(W_23,e_2,e_4) ),
inference(resolution,[status(thm)],[c_63843,c_48]) ).
tff(c_70984,plain,
( equalish(e_4,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[c_70977,c_64102]) ).
tff(c_71120,plain,
~ product(e_2,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_40,c_70984]) ).
tff(c_71272,plain,
( equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4892,c_71120]) ).
tff(c_71301,plain,
( equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_71272]) ).
tff(c_71302,plain,
product(e_2,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_62826,c_28,c_71301]) ).
tff(c_64099,plain,
! [Y_5] :
( ~ product(e_2,Y_5,e_4)
| product(Y_5,e_3,e_2) ),
inference(resolution,[status(thm)],[c_63843,c_6]) ).
tff(c_72461,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_71302,c_64099]) ).
tff(c_94,plain,
! [W_23,X_57,Y_58] :
( equalish(W_23,X_57)
| ~ product(W_23,e_4,Y_58)
| product(X_57,e_3,Y_58)
| product(X_57,e_2,Y_58)
| product(X_57,e_1,Y_58)
| ~ group_element(Y_58)
| ~ group_element(X_57) ),
inference(resolution,[status(thm)],[c_76,c_48]) ).
tff(c_4442,plain,
! [X_57] :
( equalish(e_4,X_57)
| product(X_57,e_3,e_4)
| product(X_57,e_2,e_4)
| product(X_57,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X_57) ),
inference(resolution,[status(thm)],[c_4406,c_94]) ).
tff(c_5170,plain,
! [X_163] :
( equalish(e_4,X_163)
| product(X_163,e_3,e_4)
| product(X_163,e_2,e_4)
| product(X_163,e_1,e_4)
| ~ group_element(X_163) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4442]) ).
tff(c_5272,plain,
! [W_17,X_163] :
( equalish(W_17,e_4)
| ~ product(X_163,e_3,W_17)
| equalish(e_4,X_163)
| product(X_163,e_2,e_4)
| product(X_163,e_1,e_4)
| ~ group_element(X_163) ),
inference(resolution,[status(thm)],[c_5170,c_44]) ).
tff(c_72546,plain,
( equalish(e_2,e_4)
| equalish(e_4,e_1)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_72461,c_5272]) ).
tff(c_72587,plain,
( equalish(e_2,e_4)
| equalish(e_4,e_1)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_72546]) ).
tff(c_72588,plain,
product(e_1,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_59042,c_36,c_28,c_72587]) ).
tff(c_73001,plain,
! [W_461] :
( equalish(W_461,e_2)
| ~ product(W_461,e_1,e_4) ),
inference(resolution,[status(thm)],[c_71302,c_48]) ).
tff(c_73004,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_72588,c_73001]) ).
tff(c_73131,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_73004]) ).
tff(c_73132,plain,
product(e_3,e_4,e_3),
inference(splitRight,[status(thm)],[c_63855]) ).
tff(c_76918,plain,
! [Y_473] :
( product(e_3,Y_473,e_1)
| ~ product(Y_473,e_4,e_3) ),
inference(resolution,[status(thm)],[c_62825,c_50]) ).
tff(c_77081,plain,
product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[c_73132,c_76918]) ).
tff(c_63932,plain,
! [W_23] :
( equalish(W_23,e_4)
| ~ product(W_23,e_3,e_1) ),
inference(resolution,[status(thm)],[c_62825,c_48]) ).
tff(c_77231,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_77081,c_63932]) ).
tff(c_77285,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_77231]) ).
tff(c_77287,plain,
~ product(e_4,e_4,e_4),
inference(splitRight,[status(thm)],[c_4129]) ).
tff(c_77520,plain,
( product(e_3,e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_1,e_4,e_4)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_2,c_77287]) ).
tff(c_77541,plain,
( product(e_3,e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_1,e_4,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_77520]) ).
tff(c_77548,plain,
product(e_1,e_4,e_4),
inference(splitLeft,[status(thm)],[c_77541]) ).
tff(c_78364,plain,
! [Z2_483] :
( ~ product(e_4,e_1,Z2_483)
| product(e_4,e_4,Z2_483) ),
inference(resolution,[status(thm)],[c_77548,c_8]) ).
tff(c_77637,plain,
! [W_23] :
( equalish(W_23,e_1)
| ~ product(W_23,e_4,e_4) ),
inference(resolution,[status(thm)],[c_77548,c_48]) ).
tff(c_78371,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[c_78364,c_77637]) ).
tff(c_78430,plain,
~ product(e_4,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_36,c_78371]) ).
tff(c_77523,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_4,c_77287]) ).
tff(c_77544,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_77523]) ).
tff(c_79038,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_78430,c_77544]) ).
tff(c_79039,plain,
product(e_4,e_2,e_4),
inference(splitLeft,[status(thm)],[c_79038]) ).
tff(c_77634,plain,
! [Y_5] :
( ~ product(e_4,Y_5,e_4)
| product(Y_5,e_1,e_4) ),
inference(resolution,[status(thm)],[c_77548,c_6]) ).
tff(c_79086,plain,
product(e_2,e_1,e_4),
inference(resolution,[status(thm)],[c_79039,c_77634]) ).
tff(c_80681,plain,
! [Y_502] :
( ~ product(e_2,Y_502,e_4)
| product(Y_502,e_4,e_2) ),
inference(resolution,[status(thm)],[c_79039,c_6]) ).
tff(c_80718,plain,
product(e_1,e_4,e_2),
inference(resolution,[status(thm)],[c_79086,c_80681]) ).
tff(c_77636,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_1,e_4,W_17) ),
inference(resolution,[status(thm)],[c_77548,c_44]) ).
tff(c_80743,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_80718,c_77636]) ).
tff(c_80784,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_80743]) ).
tff(c_80785,plain,
product(e_4,e_3,e_4),
inference(splitRight,[status(thm)],[c_79038]) ).
tff(c_80833,plain,
product(e_3,e_1,e_4),
inference(resolution,[status(thm)],[c_80785,c_77634]) ).
tff(c_82487,plain,
! [Y_513] :
( ~ product(e_3,Y_513,e_4)
| product(Y_513,e_4,e_3) ),
inference(resolution,[status(thm)],[c_80785,c_6]) ).
tff(c_82551,plain,
product(e_1,e_4,e_3),
inference(resolution,[status(thm)],[c_80833,c_82487]) ).
tff(c_82605,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_82551,c_77636]) ).
tff(c_82646,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_82605]) ).
tff(c_82647,plain,
( product(e_2,e_4,e_4)
| product(e_3,e_4,e_4) ),
inference(splitRight,[status(thm)],[c_77541]) ).
tff(c_82662,plain,
product(e_3,e_4,e_4),
inference(splitLeft,[status(thm)],[c_82647]) ).
tff(c_83664,plain,
! [Z2_521] :
( ~ product(e_4,e_3,Z2_521)
| product(e_4,e_4,Z2_521) ),
inference(resolution,[status(thm)],[c_82662,c_8]) ).
tff(c_83011,plain,
! [W_23] :
( equalish(W_23,e_3)
| ~ product(W_23,e_4,e_4) ),
inference(resolution,[status(thm)],[c_82662,c_48]) ).
tff(c_83671,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_83664,c_83011]) ).
tff(c_83730,plain,
~ product(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_40,c_83671]) ).
tff(c_287,plain,
! [Y_94,Y_95,X_96] :
( product(e_4,Y_94,Y_95)
| ~ product(Y_94,X_96,e_4)
| product(X_96,e_3,Y_95)
| product(X_96,e_2,Y_95)
| product(X_96,e_1,Y_95)
| ~ group_element(Y_95)
| ~ group_element(X_96) ),
inference(resolution,[status(thm)],[c_76,c_50]) ).
tff(c_293,plain,
! [X_3,Y_95] :
( product(e_4,X_3,Y_95)
| product(e_4,e_3,Y_95)
| product(e_4,e_2,Y_95)
| product(e_4,e_1,Y_95)
| ~ group_element(Y_95)
| product(X_3,e_3,e_4)
| product(X_3,e_2,e_4)
| product(X_3,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X_3) ),
inference(resolution,[status(thm)],[c_4,c_287]) ).
tff(c_83911,plain,
! [X_522,Y_523] :
( product(e_4,X_522,Y_523)
| product(e_4,e_3,Y_523)
| product(e_4,e_2,Y_523)
| product(e_4,e_1,Y_523)
| ~ group_element(Y_523)
| product(X_522,e_3,e_4)
| product(X_522,e_2,e_4)
| product(X_522,e_1,e_4)
| ~ group_element(X_522) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_293]) ).
tff(c_83923,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_83911,c_77287]) ).
tff(c_84085,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_83923]) ).
tff(c_84086,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_83730,c_84085]) ).
tff(c_84233,plain,
product(e_4,e_1,e_4),
inference(splitLeft,[status(thm)],[c_84086]) ).
tff(c_83008,plain,
! [Y_5] :
( ~ product(e_4,Y_5,e_4)
| product(Y_5,e_3,e_4) ),
inference(resolution,[status(thm)],[c_82662,c_6]) ).
tff(c_84276,plain,
product(e_1,e_3,e_4),
inference(resolution,[status(thm)],[c_84233,c_83008]) ).
tff(c_85618,plain,
! [Y_533] :
( ~ product(e_1,Y_533,e_4)
| product(Y_533,e_4,e_1) ),
inference(resolution,[status(thm)],[c_84233,c_6]) ).
tff(c_85649,plain,
product(e_3,e_4,e_1),
inference(resolution,[status(thm)],[c_84276,c_85618]) ).
tff(c_83010,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_3,e_4,W_17) ),
inference(resolution,[status(thm)],[c_82662,c_44]) ).
tff(c_85670,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_85649,c_83010]) ).
tff(c_85706,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_85670]) ).
tff(c_85707,plain,
product(e_4,e_2,e_4),
inference(splitRight,[status(thm)],[c_84086]) ).
tff(c_85751,plain,
product(e_2,e_3,e_4),
inference(resolution,[status(thm)],[c_85707,c_83008]) ).
tff(c_86964,plain,
! [Y_542] :
( ~ product(e_2,Y_542,e_4)
| product(Y_542,e_4,e_2) ),
inference(resolution,[status(thm)],[c_85707,c_6]) ).
tff(c_86995,plain,
product(e_3,e_4,e_2),
inference(resolution,[status(thm)],[c_85751,c_86964]) ).
tff(c_87016,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_86995,c_83010]) ).
tff(c_87052,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_87016]) ).
tff(c_87053,plain,
product(e_2,e_4,e_4),
inference(splitRight,[status(thm)],[c_82647]) ).
tff(c_87840,plain,
! [Z2_549] :
( ~ product(e_4,e_2,Z2_549)
| product(e_4,e_4,Z2_549) ),
inference(resolution,[status(thm)],[c_87053,c_8]) ).
tff(c_87143,plain,
! [W_23] :
( equalish(W_23,e_2)
| ~ product(W_23,e_4,e_4) ),
inference(resolution,[status(thm)],[c_87053,c_48]) ).
tff(c_87847,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_2,e_4) ),
inference(resolution,[status(thm)],[c_87840,c_87143]) ).
tff(c_87906,plain,
~ product(e_4,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_38,c_87847]) ).
tff(c_88009,plain,
! [X_550,Y_551] :
( product(e_4,X_550,Y_551)
| product(e_4,e_3,Y_551)
| product(e_4,e_2,Y_551)
| product(e_4,e_1,Y_551)
| ~ group_element(Y_551)
| product(X_550,e_3,e_4)
| product(X_550,e_2,e_4)
| product(X_550,e_1,e_4)
| ~ group_element(X_550) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_293]) ).
tff(c_88020,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_88009,c_77287]) ).
tff(c_88173,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_88020]) ).
tff(c_88174,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_87906,c_88173]) ).
tff(c_88319,plain,
product(e_4,e_1,e_4),
inference(splitLeft,[status(thm)],[c_88174]) ).
tff(c_87140,plain,
! [Y_5] :
( ~ product(e_4,Y_5,e_4)
| product(Y_5,e_2,e_4) ),
inference(resolution,[status(thm)],[c_87053,c_6]) ).
tff(c_88362,plain,
product(e_1,e_2,e_4),
inference(resolution,[status(thm)],[c_88319,c_87140]) ).
tff(c_89588,plain,
! [Y_562] :
( ~ product(e_1,Y_562,e_4)
| product(Y_562,e_4,e_1) ),
inference(resolution,[status(thm)],[c_88319,c_6]) ).
tff(c_89619,plain,
product(e_2,e_4,e_1),
inference(resolution,[status(thm)],[c_88362,c_89588]) ).
tff(c_87142,plain,
! [W_17] :
( equalish(W_17,e_4)
| ~ product(e_2,e_4,W_17) ),
inference(resolution,[status(thm)],[c_87053,c_44]) ).
tff(c_89640,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_89619,c_87142]) ).
tff(c_89676,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_89640]) ).
tff(c_89677,plain,
product(e_4,e_3,e_4),
inference(splitRight,[status(thm)],[c_88174]) ).
tff(c_89721,plain,
product(e_3,e_2,e_4),
inference(resolution,[status(thm)],[c_89677,c_87140]) ).
tff(c_91306,plain,
! [Y_572] :
( ~ product(e_3,Y_572,e_4)
| product(Y_572,e_4,e_3) ),
inference(resolution,[status(thm)],[c_89677,c_6]) ).
tff(c_91378,plain,
product(e_2,e_4,e_3),
inference(resolution,[status(thm)],[c_89721,c_91306]) ).
tff(c_91759,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_91378,c_87142]) ).
tff(c_91797,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_91759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.14/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 21:55:45 EDT 2023
% 0.14/0.36 % CPUTime :
% 25.35/11.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.35/11.95
% 25.35/11.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.74/12.02
% 25.74/12.02 Inference rules
% 25.74/12.02 ----------------------
% 25.74/12.02 #Ref : 0
% 25.74/12.02 #Sup : 15558
% 25.74/12.02 #Fact : 68
% 25.74/12.02 #Define : 0
% 25.74/12.02 #Split : 17
% 25.74/12.02 #Chain : 0
% 25.74/12.02 #Close : 0
% 25.74/12.02
% 25.74/12.02 Ordering : KBO
% 25.74/12.02
% 25.74/12.02 Simplification rules
% 25.74/12.02 ----------------------
% 25.74/12.02 #Subsume : 2577
% 25.74/12.02 #Demod : 18946
% 25.74/12.02 #Tautology : 4950
% 25.74/12.02 #SimpNegUnit : 4466
% 25.74/12.02 #BackRed : 0
% 25.74/12.02
% 25.74/12.02 #Partial instantiations: 0
% 25.74/12.02 #Strategies tried : 1
% 25.74/12.02
% 25.74/12.02 Timing (in seconds)
% 25.74/12.02 ----------------------
% 25.74/12.02 Preprocessing : 0.45
% 25.74/12.02 Parsing : 0.25
% 25.74/12.02 CNF conversion : 0.03
% 25.74/12.02 Main loop : 10.43
% 25.74/12.02 Inferencing : 1.36
% 25.74/12.02 Reduction : 2.16
% 25.74/12.02 Demodulation : 1.33
% 25.74/12.02 BG Simplification : 0.13
% 25.74/12.02 Subsumption : 6.30
% 25.74/12.02 Abstraction : 0.20
% 25.74/12.02 MUC search : 0.00
% 25.74/12.02 Cooper : 0.00
% 25.74/12.02 Total : 11.00
% 25.74/12.02 Index Insertion : 0.00
% 25.74/12.02 Index Deletion : 0.00
% 25.74/12.02 Index Matching : 0.00
% 25.74/12.02 BG Taut test : 0.00
%------------------------------------------------------------------------------